Using the methods developed in an earlier paper [J. Algebra 266, No. 2, 446–493 (2003; Zbl 1036.20049)], the author is able to prove that there are uncountably many e-varieties of orthodox semigroups between the e-variety \(\mathcal B\) of all bands and the e-variety \(\mathcal{OLB}\) of all orthodox locally idempotent semigroups. – The (technically difficult) proof is by the construction of an infinite set of identities which are independent modulo \(\mathcal{OLB}\), that is, any two distinct sets of these identities define distinct sub-e-varieties of \(\mathcal{OLB}\).